Microfluidic active mixing nozzle for three-dimensional printing of viscoelastic inks

ABSTRACT

The present disclosure relates to a device for three-dimensional ink deposition from an impeller-driven active mixing microfluidic printing nozzle. The device is configured to receive a material property associated with the plurality of fluids and receive a structure property of the printing nozzle. The device then determines a threshold relation between a rotating speed Ω of an impeller in the nozzle and a volumetric flow rate Q of fluids that flow through the nozzle based on the material property of the plurality of fluids, the structure property of the printing nozzle. Based on the threshold relation, the device then determines an actual volumetric flow rate of the fluids and actual rotation speed of the impeller.

PRIORITY STATEMENT

This application is a filing under 35 U.S.C. § 371 of InternationalPatent Application PCT/US2016/026412, filed Apr. 7, 2016, which claimspriority to US Provisional Application 62/144,078, filed Apr. 7,2015These applications are hereby incorporated by reference in theirentireties.

FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under contract numberDE-AC52-07NA27344 and DE-SC0001293 awarded by the Department of Energy.The government has certain rights in the invention.

TECHNICAL FIELD

The present disclosure generally relates to three-dimensional (3D)printing technology. Specifically, the present disclosure relates to amicrofluidic active mixing nozzle for 3D printing of viscoelastic inks.

BACKGROUND

3D printing, also known as additive manufacturing, is a revolutionary,cutting edge technology that frees product design from limitations oftraditional manufacturing technologies. 3D printing typically includesusing a nozzle to deposit successive layers of a material under computercontrol. Because a product is manufactured layer by layer, the productcan be of almost any shape or geometry. In addition, the product can befabricated from any of a number of materials that can be prepared in theform of an ink having suitable rheological properties for extrusionthrough the nozzle and deposition on a substrate. Traditionally,multiple materials have been deposited by 3D printing using more thanone nozzle in a serial or parallel deposition process.

SUMMARY

The present disclosure relates to a device for three-dimensional inkdeposition from an impeller-driven active mixing microfluidic printingnozzle. The device is configured to receive a material propertyassociated with the plurality of fluids and receive a structure propertyof the printing nozzle. The device then determines a threshold relationbetween a rotating speed Ω of an impeller in the nozzle and a volumetricflow rate Q of fluids that flow through the nozzle based on the materialproperty of the plurality of fluids, the structure property of theprinting nozzle. Based on the threshold relation, the device thendetermines an actual volumetric flow rate of the fluids and actualrotation speed of the impeller.

According to an aspect of the present disclosure, a device may comprisea microfluidic printing nozzle and a controller in electroniccommunication with the nozzle. The nozzle may comprise a mixing chamberand an impeller rotatably disposed therein. The controller may beconfigured to: receive a material property associated with each of theplurality of fluids; receive a structure property of the printingnozzle; receive a predetermined volumetric flow rate Q of the pluralityof fluids in the mixing chamber; determine a threshold rotating speed Ωof the impeller based on the material property of the plurality offluids, the structure property of the printing nozzle, and thepredetermined volumetric flow rate Q. Further, the controller may beconfigured to introduce the plurality of fluids into the mixing chamberat the predetermined volumetric flow rate; and rotate the impeller witha rotating speed higher than the threshold rotating speed Ω to mix theplurality of fluids, thereby forming the mixed ink.

According to another aspect of the present disclosure, a method forthree-dimensional ink deposition from an impeller-driven active mixingmicrofluidic printing nozzle may comprise providing a microfluidicprinting nozzle. The nozzle may comprise a mixing chamber; and animpeller rotatably disposed in the mixing chamber to mix a plurality offluids to form a mixed ink. The method may also comprise receiving by acontroller in electrical communication with the printing nozzle: amaterial property associated with each of the plurality of fluids; astructure property of the printing nozzle; a predetermined volumetricflow rate Q of the plurality of fluids in the mixing chamber. The methodmay further comprise determining a threshold rotating speed Ω of theimpeller based on the material property of the plurality of fluids, thestructure property of the printing nozzle, and the predeterminedvolumetric flow rate Q; introducing the plurality of fluids into themixing chamber at the predetermined volumetric flow rate; and rotating,under control of the controller, the impeller with a rotating speedhigher than the threshold rotating speed Ω to mix the plurality offluids, thereby forming the mixed ink.

According to another aspect of the present disclosure, a device maycomprise a microfluidic printing nozzle and a controller in electroniccommunication with the nozzle. The nozzle may comprise a mixing chamberand an impeller rotatably disposed therein. The controller may beconfigured to: receive a material property associated with each of theplurality of fluids; receive a structure property of the printingnozzle; receive a predetermined rotating speed Ω of the impeller;determine a threshold volumetric flow rate Q of the plurality of fluidsin the mixing chamber based on the material property of the plurality offluids, the structure property of the printing nozzle, and thepredetermined rotating speed of the impeller; introduce the plurality offluids into the mixing chamber at volumetric flow rate lower than thethreshold volumetric flow rate Q; and rotate the impeller at thepredetermined rotating speed Ω to mix the plurality of fluids, therebyforming the mixed ink.

According to yet another aspect of the present disclosure, a method forthree-dimensional ink deposition from an impeller-driven active mixingmicrofluidic printing nozzle may comprise providing a microfluidicprinting nozzle comprising a mixing chamber and an impeller rotatablydisposed in the mixing chamber to mix a plurality of fluids to form amixed ink. The method may also comprise receiving by a controller inelectrical communication with the printing nozzle: a material propertyassociated with the plurality of fluids; a structure property of theprinting nozzle; a predetermined rotating speed Ω of the impeller;determining a threshold volumetric flow rate Q of the plurality offluids in the mixing chamber based on the material property of theplurality of fluids, the structure property of the printing nozzle, andthe predetermined rotating speed of the impeller; introducing theplurality of fluids into the mixing chamber at volumetric flow ratelower than the threshold volumetric flow rate Q; and rotating theimpeller at the predetermined rotating speed Ω to mix the plurality offluids, thereby forming the mixed ink.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram illustrating a 3D printer with amicrofluidic active mixing nozzle according to exemplary embodiments ofthe present application;

FIG. 2 is a schematic diagram illustrating an exemplary embodiment of aserver;

FIG. 3 is a flowchart illustrating a method for actively mixing multiplemicro-fluids with the microfluidic active mixing nozzle;

FIG. 4A is a schematic illustration of passive and active mixing nozzledesigns;

FIG. 4B is an operating map for mixing behavior of the passive andactive mixing nozzle designs;

FIG. 5A illustrates an experimenting result of mixing Newtonian liquidsin an active mixing chamber;

FIG. 5B illustrates an experimental result of mixing non-Newtonianliquids in the active mixing chamber;

FIG. 6 illustrates a mixing efficiency against mixing ratio for fourdifferent flow rates;

FIG. 7A shows optical images of a printed 2D carpet structures showing acontinuously varying color gradient and a discrete change in color dueto different amounts of pigment;

FIG. 7B shows images of a cross-section of 3D rectangular latticestructures showing continuous and discrete changes in color;

FIG. 7C illustrates 3D printing of a two-part epoxy honeycomb structure;

FIG. 8A illustrates mixing result in a passive mixing chamber withsmooth wall;

FIG. 8B illustrates mixing result in a passive mixing chamber withgrooved wall;

FIG. 9A is an optical image of a passive mixing chamber;

FIG. 9B is an optical image of an active mixing chamber;

FIG. 10 illustrates rheological flow curves of three ink formulationsused in calibration tests in example embodiments;

FIGS. 11A-11C show measurements of a diffusion coefficient of a IFWB-C7dye;

FIG. 12A is a picture of a superstructure used to hold the nozzle duringprinting; and

FIG. 12B is a magnified image of the metal nozzle used for printing aviscous two-part epoxy.

DETAILED DESCRIPTION

Mixing fluids at low-Reynolds number is fundamental for a broad range ofscientific and industrial applications from bioassays, to medicalanalysis, and additive manufacturing. In the latter case, direct inkwrite (DIW) 3D printing is a powerful fabrication technique, which maybe implemented in a multi-material mode to fabricate composite materialswith added functionality, such as heterogeneous hydrogel scaffolds,cell-laden tissue constructs, optical waveguides, structural epoxies andhighly aligned nanowire fibers. A major challenge for multi-material 3Dprinting is ensuring uniform mixing of highly viscoelastic inks in lowvolumes and short time scales. Passive mixing in microfluidic devicesvia chaotic stirring or secondary flows may be limited to low viscosityNewtonian fluids with diffusive colloidal particles, strongly hinderingthe advancement of research for a broad palette of functional materialsand their applications.

The present disclosure provides a microfluidic active mixing nozzle andmethods for actively mixing a plurality of fluids in a microchannel.Using these methods, the microfluidic nozzle may be able to uniformlymix diffusive and non-diffusive particles in Newtonian and non-Newtonianinks over a wide range of operating conditions. Various aspects of 3Dprinting are set forth in detail in the following patent publications,all of which are hereby incorporated by reference in their entirety:PCT/US2014/043860, filed Jun. 24, 2014, PCT/US2014/063810, filed Nov. 4,2014, PCT/US2014/065899, filed Nov. 17, 2014, and PCT/US2015/015148,filed Feb. 10, 2015. The nozzle and method described herein may in someembodiments have one or more features described in these priorpublications.

FIG. 1 is a schematic diagram illustrating a 3D printer 100 according toexemplary embodiments of the present disclosure. The 3D printer 100 mayinclude a microfluidic active mixing nozzle 118 (“the nozzle”), aplurality of fluid sources 104, 106, a motor 108, an actuator 130, andan electronic controller 102.

The nozzle 118 may include a mixing chamber 120 and an impeller 110. Themixing chamber 120 may be of a cylindrical or prismatic shape with ahydraulic diameter (i.e., effective diameter) d (e.g., d=4 mm, and themixing chamber has a volume of 150 μL). The inner surface of the mixingchamber may be sufficiently smooth that a fluid flowing through themixing chamber 120 exhibits laminar flow. Alternatively, the innersurface of the mixing chamber may be sufficiently grooved or coarse thefluid flowing through the mixing chamber 120 exhibits chaotic flow.

The mixing chamber 120 may include a plurality of inlets 122, 124. Forexample, the mixing chamber 120 may include two inlets 122, 124 at oneend. Each inlet 122, 124 may be configured to connect with an ink sourcecontaining a fluidic ink. For example, in FIG. 1, the first inlet 122may be connected to a first ink source 104 containing a first ink 112,and the second inlet 124 may be connected to a second ink source 106containing a second ink 114. Each ink source 104, 106 may beelectronically connected to a controller 102, which may control the inksource to inject and/or introduce the corresponding inks 112, 114 intothe mixing chamber 120 at a controlled volumetric flow rate. The ink maybe any applicable fluid. For example, the ink may comprise aviscoelastic fluid, such as a surfactant solution, lubricant gel, orelastomeric ink (e.g., SE 1700). Examples of the inks and theircorresponding material properties are shown in Table 1.

TABLE 1 η ρ

T_(y) K [Pa.s] [kg/m3] [μm2/s] [Pa] [Pa.sn] n Water 0.001 1000 500Water:Glycerol 0.054 1200 9.3 [20:80 wt %] Glycerol 1.2 1250 0.41Lubricant Gel 1000 280 20 20 0.44 Pluronic 1050 20 500 2 0.85 SE 17001400 180 0.65

The mixing chamber 120 may also include an outlet 126. The outlet may belocated at the other end of the mixing chamber 120 opposite to theinlets 122, 124 may have a diameter a (e.g., a=500 μm). When the inksource 104, 106 introduces a plurality of inks 112, 114 into the mixingchamber 120, the inks may flow through the mixing chamber 120, undergoactive mixing by the impeller 110, and exit the mixing chamber 120through the outlet 126 as a mixed ink.

The impeller 110 may be rotatably and coaxially disposed in the mixingchamber 120. It may have a cylindrical or prismatic shape with ahydraulic diameter δ (e.g., δ=2.7 mm). The hydraulic diameter δ may beslightly smaller than the hydraulic diameter d of the mixing chamber120, so that there is a small gap between the mixing chamber 120 and theimpeller 110. Further, the mixing chamber 120 and the impeller 110 mayform an effective mixing length l (e.g., l=30 mm) therebetween along theaxis X-X. In the event that the length of the impeller 110 substantiallyequals the length of the mixing chamber 120, the effective length l maybe equal to a length of the mixing chamber 120, as shown in FIG. 1.

The impeller 110 may be connected to a motor 108, which may beelectronically in communication with and under control of the controller102. Consequently, the controller 102 may be able to control the motor108 to drive the impeller 110 to rotate at a desired speed Ω.Accordingly, when the plurality of fluidic inks 112, 114 flow throughthe gap between the inner surface of the mixing chamber 120 and outersurface of the impeller 110, rotating the impeller 110 may actively mixthe plurality of fluidic inks 112, 114.

The surface of the impeller 110 may be smooth, grooved and/or containprotrusions. For example, in FIG. 1, the surface of the impeller 110includes a spiral protrusion 116 to facilitate mixing of the pluralityof fluidic inks 112, 114 as they flow through the mixing chamber 120. Anadvantage of active mixing is decoupling the mixing process from theflow rate and mixing geometry; thus, mixing of ideally any type offluidic inks 112, 114 may be achieved with low residence time (i.e., atime needed to flow through the mixing chamber 120), pressure losses andmixing volumes.

In addition to the nozzle 118, the plurality of fluid sources 104, 106,the motor 108, and the electronic controller 102, the 3D printer 100 mayalso include an actuator 130 mechanically connected to the nozzle 118.The actuator 130 may be any type of mechanical structure that canprovide linear and/or rotational motion to the nozzle 118. For example,the actuator 130 may be a carriage rail structure typically used ininkjet printers. The nozzle may be mechanically mounted on a carriagerail 132. A carriage motor 134 may be configured to drive a belt or athread to move the nozzle 118 along the x, y, and/or z direction. Bymoving the nozzle 118 with a predetermined and controlled path, the 3Dprinter may be able to deposit the mixed fluidic ink that flows out ofthe outlet 126 at a predetermined pattern on a substrate 128, which isplaced on a platform 132 of the 3D printer 100.

Alternatively, the platform 132 may be mechanically connected to theactuator 130. The 3D printer 100 may be able to deposit the mixedfluidic ink with the predetermined pattern by moving the platform 132along the x, y, and/or z direction.

FIG. 2 is a schematic diagram illustrating an exemplary embodiment of anelectronic controller 102. The electronic controller may be a speciallydesigned electronic device for controlling the 3D printer 100 or may bea computer implementing special applications for controlling the 3Dprinter 100. The controller may be configured for wired or wirelesscommunication with the 3D printer 100. The controller 102 may varywidely in configuration or capabilities, but it may include one or morecentral processing units 222 and memory 232, at least one medium 230(such as one or more transitory and/or non-transitory mass storagedevices) for storing application programs 242 or data 244 that maycontrol components of the 3D printer 100. The processing units 222 mayexecute the application programs 242 or data 244 to perform thecontrolling methods disclosed in the present disclosure.

The controller 102 may further include one or more power supplies 226,one or more wired or wireless network interfaces 250, one or moreinput/output interfaces 258, and/or one or more operating systems 241,such as Windows Server™, Mac OS X™, Unix™, Linux™, FreeBSD™, or thelike. Thus a controller 102 may include, as examples, industrialprogrammable motor controllers with or without a graphical userinterface, dedicated rack-mounted servers, desktop computers, laptopcomputers, set top boxes, mobile computational devices such as smartphones, integrated devices combining various features, such as two ormore features of the foregoing devices, or the like.

FIG. 3 is a flowchart illustrating a method for actively mixing multiplemicro-fluids with the microfluidic active mixing nozzle 118. The methodmay be implemented using the 3D printer 100. For example, the method maybe implemented as a set of instructions stored in the storage medium 230and may be executed by the processor 222 of the controller 102. Themethod may include the following operations:

In 302, the controller receives a material property associated with eachof a plurality of fluids and a predetermined degree of mixture of theplurality of fluids. For example, the plurality of fluids may be firstink 112 and a second ink 114.

The degree of mixture may reflect a degree of completeness to which theplurality of fluids may be mixed in the mixing chamber 120. It may beexpressed by a degree of mixture coefficient ε, which is defined as

${ɛ \equiv \frac{s_{f} - s_{u}}{s_{m} - s_{u}}},$wherein s_(f) is a measurement of Shannon entropy index of particledistributions across the width of the mixed ink filament extruded fromthe nozzle; s_(m) is the entropy of a hypothetically perfectly mixedfilament; and s_(u) is the entropy of a completely unmixed filament.Alternatively, the value of degree of mixture coefficient ε may beobtained empirically and may be stored in the storage medium of thecontroller 102 as a database. For example, for a complete mixture, ε=1;and for completely unmixed fluids ε=0.

The plurality of fluids may be compatible with each other so that mixingthereof is possible. In an exemplary embodiment, the first ink 112 maybe a carrier fluid (e.g., water) and the second ink 114 may be aconcentrated dye solution (e.g., dye particle in water). In anotherexemplary embodiment, the first and second inks may be a two-part epoxy,e.g., the first ink 112 may be a resin and the second ink 114 may be acuring agent.

The material property may include whether a fluid of the plurality offluids contains Brownian or non-Brownian particles. It may also includea diffusion transport coefficient

of the particles plurality of fluids. The diffusion transportcoefficient

may be molecular diffusion coefficient of a particle (of a given typeand size) of a fluid in a carrier fluid. For example, the diffusiontransport rate

may be the molecular diffusion coefficient of a dye particle in thesecond ink 114 in the water of the first ink 112; or the diffusiontransport coefficient

may be the molecular diffusion coefficient of a particle of the curingagent in the resin. The value of

for a given particle may be different in different carrier fluids. Whenthe viscosity of each of the plurality of fluids is substantially thesame, the diffusion transport coefficient

among the plurality of fluids may be substantially the same. Forexample, the diffusion transport rate of a water-based dye solution towater may be substantially the same as the diffusion transport rate ofthe water to the water-based dye solution. Alternatively, when theplurality of fluids have different viscosities, the diffusion transportrate (i.e., first diffusion transport rate) of a first fluid in a secondfluid may be different from the diffusion transport rate (i.e., seconddiffusion transport rate) of the second fluid in the first fluid. Forexample, the first diffusion transport rate may be 3 times or even morethan the second diffusion transport rate. Mixing fluids with similardiffusion transport rates is generally easier than mixing fluids withdifferent diffusion transport rates.

The material property of the plurality of fluids may be manually inputby a user of the 3D printer 100. Alternatively, the material property ofthe plurality of fluids may be automatically and/or dynamicallyobtained. For example, the controller 102 may include a data base ofdifferent fluids in its storage medium. Once the identities of the firstink 112 and the second ink 114 are input by the user and/or detected bya sensor in the ink sources 104, 106, the controller 102 may search thedatabase and automatically obtain the material property of the first andsecond inks 112, 114.

In 304, the controller receives a structure property of the printingnozzle.

The structure property of the nozzle may include the hydraulic diameterd of the mixing chamber 120, the hydraulic diameter δ of the impeller,and the effective mixing length l of the mixing nozzle. The diameter δof the impeller may be slightly smaller than the diameter d of themixing chamber 120, as described above. Further, when the length of themixing chamber 120 is substantially the same length of the impeller, thelength of the chamber is substantially the same as the effective lengthl.

The structure property of the nozzle may also include surfacecharacteristics of the mixing chamber 120 and the impeller 110. Forexample, the mixing chamber 120 and/or the impeller 110 may have smoothsurfaces to enable laminar flow of the plurality of fluids or may begrooved or with protrusions 116 to enable chaotic flow to the pluralityof fluids.

In 306, based on the material property of the plurality of fluids andthe structure property of the nozzle, the controller 102 determines arelationship between a volumetric flow rate Q of the plurality of fluidsin the mixing chamber 120 and a rotating speed Ω of the impeller.

In order to mix Brownian fluids (liquids laden with Brownian particles)when the mixing chamber 120 is smooth enough to enable laminar flow, theminimum residence timescale t_(res) of a fluid element in the mixingchamber 120 must exceed a time t_(mix) required for the particles todiffuse over a characteristic distance set by the flow dynamics withinthe mixing chamber 120. Without the impeller 110, when the mixingchamber 120 is smooth enough to enable laminar flow, two streamsconverge into a single rectilinear channel of length l and hydraulicdiameter d. An efficient mixing of the two streams may require thatl/d≳Pe/N ²  (1)where Pe is the Péclet number defined as Pe≡Q/d

, Q is volumetric flow rate of the whole mixed streams through themixing chamber 120, and N is a number of layers of the plurality offluids formed in the mixing chamber 120.

With an impeller-driven active mixing, when the impeller 110 rotates atrotation speed Ω, the residence time is given by t_(res)˜l(d²−δ²)/Q. Therapid motion of the impeller induces a shear rate {dot over(γ)}=δΩ/(d−δ) that is independent from the volumetric flow rate Q.Furthermore, the effective diffusion distance is some fraction of themixing chamber diameter d_(eff)˜d/m, where m˜Ωt_(res) is proportional tothe number of revolutions completed by the impeller while a fluidelement resides in the mixing chamber 120. By equating the twotimescales, the relation between the volumetric flow rate Q and therotation speed Ω of the impeller may bear a relation as, in adimensionless form,

$\begin{matrix}{\frac{l}{d} > {c_{1}ɛ\;\frac{{Pe}^{3}}{\alpha^{3}{\overset{\sim}{\Omega}}^{2}}}} & (2)\end{matrix}$where the dimensionless rotation rate is {tilde over (Ω)}≡ldΩ/

, α≡1−δ²/d², c₁ is a constant value, and ε is the degree of mixturecoefficient.

For Brownian fluids and when surfaces of the mixing chamber 120 and theimpeller 110 are configured to enable a chaotic flow, such as when theinner wall of the mixing chamber 120 is grooved and/or when the impelleris grooved and/or includes protrusions 116, without rotation of theimpeller 110, the effective mixing distance is d_(eff)˜d/2^(n), where nis proportional to the number of grooves in the mixing chamber. Themixing timescale is therefore t_(mix)˜d_(eff) ²/

. Accordingly, efficient mixing of the plurality of fluids ma requirethatl/d≳ln(Pe)  (3)

With an impeller-driven active mixing, when the impeller 110 rotates atrotation speed Ω, if the impeller is grooved and induces chaoticadvection within the mixing chamber, then the effective diffusion lengthis d_(eff)˜d/2^(m), in which case the volumetric flow rate Q and theimpeller rotation speed Ω may bear a relation of,

$\begin{matrix}{\frac{l}{d} > {\frac{c_{2}ɛ\; P\; e}{\alpha}4^{{- \overset{\sim}{\Omega}}\;{\alpha/{Pe}}}}} & (4)\end{matrix}$wherein c₂ is a constant.

The plurality of fluids may comprise non-Brownian fluids, such as highlyelastic inks or pastes with large filler material, e.g., pigments orfibers, for which thermal motion is negligible. Because moleculardiffusion cannot mix these particles, uniform homogenization occurs onlyif the final length scale of interdigitation between the incomingstreams reaches the order of the particle size d_(p)˜d/2^(m). Followingsimilar reasoning used to derive Eq. (2) and (4), the ratio of theimpeller rotation speed Ω and the volumetric flow rate Q of theplurality of fluids may be expressed as

$\begin{matrix}{\frac{{ld}^{2}\Omega}{Q} > {c_{3}{ɛln}\frac{d}{d_{p}}}} & (5)\end{matrix}$wherein c₃ is a constant.

In 308, based on the relationship, the controller 102 determines athreshold combination of the volumetric flow rate Q of the plurality offluids and the rotation speed Ω of the impeller.

In 310, the controller 102 controls the 3D printer to introduce theplurality of fluids into the mixing chamber 120 at a volumetric flowrate Q′ and to rotate the impeller with a rotation speed Ω′ to mix theplurality of fluids, thereby forming the mixed ink. The actualvolumetric flow rate Q′ and the actual impeller rotation speed Ω′ are soselected so that a ratio thereof is lower than or equal to a ratio ofthe threshold volumetric flow rate Q over the threshold rotating speedΩ, i.e.,

$\begin{matrix}{\frac{Q^{\prime}}{\Omega^{\prime}} \leq {\frac{Q}{\Omega}.}} & (6)\end{matrix}$

According to an exemplary embodiment of the present disclosure, thecontroller 102 may receive a predetermined volumetric flow rate Q of theplurality of fluids as a whole in the mixing chamber 120. And then thecontroller 102 may determine a threshold rotating speed Ω of theimpeller based on the material property of the plurality of fluids, thestructure property of the printing nozzle, and the predeterminedvolumetric flow rate Q.

To this end, the controller may determine the nature of the plurality offluids and whether the mixing chamber 120 and the impeller 110 areconfigured to enable laminar flow or chaotic flow of the plurality offluids. When the plurality of fluids are Brownian fluids and when boththe mixing chamber 120 and the impeller 110 are smooth enough forlaminar flow, the controller 102 may determine a threshold rotationspeed of the impeller 110 based on Eq. (2), which takes a form of:

$\begin{matrix}{\Omega = {\frac{Q}{\alpha\;{ld}^{2}}{\sqrt{\frac{{c\;}_{1}ɛ\; Q}{\alpha\; l\;{??}}}.}}} & (7)\end{matrix}$

When the plurality of fluids are Brownian fluids and when one or both ofthe mixing chamber 120 and the impeller 110 are grooved or includeprotrusions, so that the plurality of fluids exhibit chaotic flow whenflowing through the gap between the inner surface of the mixing chamber120 and the impeller 110, the controller 102 may determine the thresholdrotation speed of the impeller 110 based on Eq. (4), which takes a formof:

$\begin{matrix}{\Omega = {\frac{Q}{\alpha\;{{ld}\;}^{2}}\log_{4}{\frac{{c\;}_{2}ɛ\; Q}{\alpha\; l\;{??}}.}}} & (8)\end{matrix}$

When at least one of the plurality of fluids is a non-Brownian fluid,the controller 102 may determine the threshold rotation speed of theimpeller 110 based on Eq. (5), which takes a form of

$\begin{matrix}{{\Omega = {\frac{{c\;}_{3}ɛ\; Q}{\alpha\; l\; d^{2}}\ln\frac{d}{d_{p}}}},} & (9)\end{matrix}$wherein d_(p) is the particle size of the non-Brownian fluid.

After the threshold impeller rotation speed is determined, thecontroller 102 may control the ink sources 104, 106 to introduce theplurality of fluids into the mixing chamber 120 at the predeterminedvolumetric flow rate Q and control the motor 108 to rotate the impellerat a rotating speed Ω′ higher than the threshold rotation speed Ω to mixthe plurality of fluids.

According to another exemplary embodiment of the present disclosure, thecontroller 102 may first receive a predetermined rotating speed Ω of theimpeller 110. And then the controller 102 may determine a thresholdvolumetric flow rate Q of the plurality of fluids as a whole in themixing chamber 120 based on the material property of the plurality offluids, the structure property of the printing nozzle, and thepredetermined rotating speed Ω.

To this end, the controller may determine the nature of the plurality offluids and whether the mixing chamber 120 and the impeller 110 areconfigured to enable laminar flow or chaotic flow of the plurality offluids. When the plurality of fluids are Brownian fluids and when boththe mixing chamber 120 and the impeller 110 are smooth enough for alaminar flow, the controller 102 may determine the threshold volumetricflow rate Q of the plurality of fluids based on Eq. (2), which takes aform of

$\begin{matrix}{Q = {\alpha\;{{ld} \cdot {\sqrt[3]{\frac{d\;{??}\;\Omega^{2}}{c_{1}ɛ}}.}}}} & (10)\end{matrix}$

When the plurality of fluids are Brownian fluids and when one or both ofthe mixing chamber 120 and the impeller 110 are grooved or includeprotrusions, so that the plurality of fluids may exhibit chaotic flowwhen flowing through the gap between the mixing chamber 120 and theimpeller 110, the controller 102 may determine the threshold volumetricflow rate Q of the plurality of fluids based on Eq. (4), which takes aform of

$\begin{matrix}{{Q\;\log_{4}\frac{{c\;}_{2}ɛ\; Q}{\alpha\; l\;{??}}} = {\alpha\;{ld}^{\; 2}{\Omega.}}} & (11)\end{matrix}$

When at least one of the plurality of fluids is non-Brownian fluid, thecontroller 102 may determine the threshold volumetric flow rate Q of theplurality of fluids based on Eq. (5), which takes a form of

$\begin{matrix}{Q = {\frac{\alpha\;{ld}^{2}}{c_{3}ɛ}\ln{\frac{d_{p}}{d} \cdot {\Omega.}}}} & (12)\end{matrix}$

After the threshold volumetric flow rate Q of the plurality of fluids isdetermined, the controller 102 may control the motor 108 to rotate theimpeller at the predetermined rotating speed 12 and control the inksources 104, 106 to introduce the plurality of fluids into the mixingchamber 120 at a total volumetric flow rate Q′ that is lower than thethreshold volumetric flow rate Q to mix the plurality of fluids.

In the event that a varying degree of mixture and/or varying mixingspeed is required, the controller 102 may determine a correspondingvariation of the threshold volumetric flow rate and/or impeller rotationspeed. For example, when the first ink 112 is a curing agent and thesecond ink 114 is a resin, the controller 112 may dynamically receive arequest for varying epoxy feeding speed (volumetric flow rate) andvarying degree of mixture from a user, and may dynamically determine thecorresponding impeller rotation speed. Consequently, the nozzle may beable to dynamically provide the mixed epoxy with the required degree ofmixture and feeding speed.

In 312, the controller may control the nozzle to extrude a continuousfilament of the mixed ink on a substrate. By moving the nozzle 118 orthe platform 132 or both along a predetermined way, the 3D printer 100may be able to layer by layer print a 3D structure as designed. Forexample, the 3D printer 100 may use an elastomeric ink, such aspolydimethylsiloxane (e.g. SE 1700), to print materials with localvariations in mechanical properties (such as elastic modulus) forapplications including soft robotics and flexible electronics

FIG. 4A is a schematic comparison of mixing nozzle designs for passiveand active mixing chambers using laminar and chaotic flow. FIG. 4B is anoperating map for mixing nozzles. As can be seen from the figures, theboundaries between regimes of good (shaded) and poor (unshaded) mixingare given by the curves, wherein the solid lines correspond to passivemixing (without impeller) of the same row in FIG. 4A and the dashedlines corresponds to active mixing (with impeller) of the same row inFIG. 4A. Correspondingly, the mixing nozzle design (a) shown in FIG. 4Acorresponds with zone (a) of the operating map in FIG. 4B; the mixingnozzle design (b) shown in FIG. 4A corresponds with zone (b) of theoperating map in FIG. 4B; the mixing nozzle design (c) shown in FIG. 4Acorresponds with zone (c) of the operating map in FIG. 4B; and themixing nozzle design (d) shown in FIG. 4A corresponds with zone (d) ofthe operating map in FIG. 4B. Further, in FIG. B, the position of theboundary for the active mixing chamber corresponds to {tilde over(Ω)}=10⁷ and can be moved by changing impeller speed. The curves for theactive mixing chamber have been calculated with α=0.54 and β=0.38.

According to exemplary embodiments of the present disclosure, threeNewtonian fluids were tested as reference materials along with severalviscoelastic inks commonly used for DIW 3D printing (Table 1). In orderto evaluate the efficiency of mixing the Brownian particles in eachnozzle, a dyed and undyed stream of the same fluid were mixed at equalflow rates (i.e. Q_(dyed)=Q_(undyed)=½Q), and the concentrationdistribution in the cross-section of the nozzle outlet was imaged. Theextent of mixing was quantified by the coefficient of variation c_(v) ofthe image intensity (c_(v)→0 with increasing homogenization), which hasbeen previously used in mixing studies in microfluidic devices.

Whereas mixing in the passive mixing chamber was governed only by Pe(FIG. 8), the mixing process in the impeller-driven active mixingchamber (IDAM) can be controlled by varying the impeller speed Ωaccording to the rewritten form of Eq. (4)

$\begin{matrix}{\overset{\sim}{\Omega} \succsim {\frac{1}{\alpha}{{{Pe}\left( {{\ln\;{Pe}} - {\ln\left( {\frac{l}{d}\alpha} \right)}} \right)}.}}} & (13)\end{matrix}$

FIG. 8 illustrates mixing results in the passive mixing chamber. Thefigure shows a plot of coefficient of variation c_(v) in the Bi-Pe phasespace for the smooth wall (FIG. 8A) and grooved wall (FIG. 8B) passivemixing chambers as determined from the color saturation images of thenozzle cross-sections for water (circle), water:glycerol [20:80 wt %](square), lubricant gel (upright triangle) and pluronic (diamond). Thesolid and hollow symbols indicate regimes of good and poor mixingrespectively, corresponding to images in which a sharp interface betweendyed and undyed streams could be visually observed. Representativegrayscale images of the color saturation are shown below each plot withbright and dark regions indicating dyed and undyed streams. The testfluids are, respectively, water (a, e), water:glycerol [20:80 wt %] (d,h), lubricant gel (b, f), and pluronic (c, g).

Hence, for a constant value of l/d, the mixing efficiency in the IDAMwas controlled by two independent parameters {tilde over (Ω)} and Pe.

FIG. 5 illustrates an experimental result of mixing in the active mixingchamber. The figure illustrates a plot of coefficient of variation c_(v)in the {tilde over (Ω)}-Pe phase space for Newtonian liquids (FIG. 5A)and yield stress fluids (FIG. 5B, non-Newtonian fluids) as determinedfrom the channel intensity of images of the nozzle cross-sections forwater (circle), water:glycerol [20:80 wt %] (square), glycerol (invertedtriangle), lubricant gel (upright triangle) and pluronic (diamond). Thesolid black curve follows the relation {tilde over (Ω)}=3 Pe(lnPe−ln(αl/d))/α, which separates the regions of good and poor mixingindicated by solid and hollow symbols respectively, corresponding toimages in which a sharp interface between dyed and undyed streams couldbe visually observed. Representative grayscale images of the colorsaturation are shown below each plot with bright and dark regionsindicating dyed and undyed streams. The color of the border indicatesthe test fluid: gold (water:glycerol [20:80 wt %]), purple (glycerol),blue (lubricant gel) and green (pluronic).

The results in FIG. 5 show that fluid inertial effects may have affectedthe mixing in water since Re≲850, but were negligible for all other testfluids since Re≲10. For all calibration experiments, the impeller shaftwith grooves but no notches (FIG. 9) was used, because the notchedimpeller induced sufficient cross-streamwise fluid motion, even for norotation (i.e. Ω=0), so as to make identification of the poor mixingregime inordinately challenging.

FIG. 9 is optical images of the mixing chambers. The passive mixingchamber (FIG. 9A) consists of a Y-type junction and a long duct ofhydraulic diameter d=500 μm and length l=15 mm. The channel surfaces ofthe passive mixing chambers are shown in the magnified image. The activemixing chamber (FIG. 9B) consists of two inlet channels connecting tothe central mixing volume of length l=30 mm, diameter d=4 mm and outletdiameter a=500 μm with the impeller of diameter δ=2.7 mm. The two typesof impellers are shown in the magnified image. An alternative designwith metal fixtures was implemented for mixing with highly viscous epoxysystems.

The c_(v) values for the Newtonian fluids of the {tilde over (Ω)}-Pephase space are plotted in FIG. 5A along with representative images ofthe nozzle cross-section for good (image a) and poor (image c) mixing.The boundary between these two regimes is delineated by the black curvegiven by {tilde over (Ω)}_(c)=3 Pe(lnPe−ln(αl/d))/α, which liesapproximately along the c_(v)-isocontour at which a distinct interfacebetween dyed and undyed streams could not be easily identified (imageb). The precise value of the proportionality coefficient (here 3) wasempirically determined for the particular IDAM used in this study andmay not always be universal for similar active mixing systems.Nevertheless, its value was of order unity, validating the applicabilityof the derivation of Eq. (4). Clearly, the IDAM could reliablyhomogenize multiple streams of Newtonian liquids over many orders ofmagnitude of Pe, corresponding to typical print speeds for DIW 3Dprinting (i.e. 0.1≤U≤100 mm/s).

Two aqueous non-Newtonian yield stress materials (FIG. 5B), which wereshown previously to mitigate the effectiveness of the passive mixingchamber (FIG. 8), were tested to evaluate the effectiveness of the IDAMfor more realistic 3D printing applications. As before, the transitionfrom uniform (image d) to poor (image f) mixing occurred at the boundary(image e) also spanned by {tilde over (Ω)}_(c)=3 Pe(ln Pe−ln(αl/d))/α.The value of Bi for the lubricant gel ranged between 0.03≤Bi≤1 and forpluronic 0.19≤Bi≤1, hence at the highest rotation rates the inks werethoroughly fluidized. The similarity in the location of the boundarybetween mixing regimes for both the Newtonian (FIG. 5A) andnon-Newtonian (FIG. 5B) liquids also suggested that the inks weresufficiently fluidized so that the precise value of Bi did not stronglyaffect the mixing efficiency of the IDAM.

Two streams of SE 1700, laden and unladen with 6-μm non-Brownianparticles, were injected into the IDAM. The Shannon entropy index of theparticle distributions across the filament width s_(f) was measuredunder fluorescence microscopy to calculate the normalized mixingefficiency defined

$\begin{matrix}{ɛ \equiv {\frac{s_{f} - s_{u}}{s_{m} - s_{u}}.}} & (14)\end{matrix}$The entropy of a hypothetically perfectly mixed filament is s_(m), andthe entropy of a completely unmixed filament is s_(u), for whichparticles are uniformly present in only half the filament width. Exampleoptical images of the particles in poorly (image a), moderately (imageb) and well (image c) mixed filaments and the plot of ε are shown inFIG. 6.

FIG. 6 illustrates a mixing efficiency ε against mixing ratio ld²Ω/Q forfour different flow rates. The solid line curve has been added to guidethe eye. Three example particle distributions in the printed filamentcorresponding to different mixing ratios are shown below the plot. Inthe images a, b, and c below the chart, the dark dots have been added toindicate the position of each tracer particle in the filament.

The entropy index followed an approximately sigmoidal profile withmixing ratio between the limits of poor and good mixing as illustratedby the solid line curve in FIG. 6, which has been added to guide theeye. The failure of ε to attain precisely its expected asymptotic valuesof zero (perfectly unmixed) and one (perfectly mixed) at respectivelylow and high dimensionless rotation speeds, may have been due to the lowparticle seeding density in the filament, which could have preventedstatistical convergence. The seeding density was selected to ensurenearly all particles in the filament were clearly visible without beingoptically obstructed by other particles lying below it. Above a criticalvalue of the mixing ratio ld²Ω/Q≳100, ε reached a plateau indicatinguniform particles dispersion in the filament. This result was inagreement with the proposed scaling relationship in Eq. (5) andindicated that the threshold for thorough mixing is given by

$\frac{{ld}^{2}\Omega}{Q} \sim {9\;{\ln\left( {d\text{/}d_{p}} \right)}\text{/}{\alpha.}}$

The IDAM was clearly capable of mixing a broad palette of materials.Therefore it was utilized for two different example applications tofurther evaluate its suitability for common types of 3D printing motifs.In the first application, the ratio of clear and pigmented material wascontrolled to vary the color of the printed structure. In the second, apolymer and cross-linking agent were mixed to create printed epoxystructures.

In the calibration measurements, the two streams were mixed in equalportion, but for the applications below, homogenization was required atratios as large as 9:1, whose effect on mixing quality was notthoroughly characterized. Hence, to ensure full mixing according to Eq.(5), low flow rates (Q≤0.3 mL/min) and nearly the maximum achievableimpeller speed (Ω=25 rad/s) were selected to ensure a large mixing ratiold²Ω/Q≥2400. Furthermore, multiple notches were added along the lengthof the impeller (FIG. 9) to introduce rotational asymmetry in eachrevolution of the impeller and thereby enhance mixing.

FIG. 7A is grey-scale optical images of a printed 2D carpet structuresshowing a continuously varying color gradient (top) and a discretechange in color due to different amounts of red pigment in SE 1700. FIG.7B is grey-scale Images of the cross-section of 3D rectangular latticestructures showing continuous (left) and discrete (right) changes incolor. FIG. 7C illustrates a 3D printing of a two-part epoxy honeycombstructure.

The color of an elastomeric ink (SE 1700) was continuously anddiscretely varied while printing 2D carpet and 3D rectangular latticestructures (FIG. 7A and FIG. 7B). A continuously varying color gradientwas created by printing a fixed amount of material at five differentmonotonically varying flow rate ratios of clear and pigmented ink. Thisprinting method was used to create the structures in FIG. 7A (top) andFIG. 7B (left) with a gradient from the purely clear to the fully red(in FIG. 7 fully dark) material. Discrete changes in color were achievedby purging the nozzle after changing to a new flow rate ratio. Thislatter printing method was used to create the structures in FIG. 7A(bottom) and FIG. 7B (right), for which the printing transitionedsequentially from fully red to pink (in FIG. 7, from dark to grey), topurely clear, again to pink and finally to fully red material (in FIG.7, from grey to dark). The color uniformity in all five layers clearlydemonstrates the ability of the IDAM to homogenize the color pigment.

The printed honeycomb structure made from a two-part epoxy is shown inFIG. 7C. A ratio of 20:80 vol % curing agent:resin was continuouslymixed during the printing. The pot-life of the epoxy at room temperaturewas 45 minutes (taken here as the time after mixing at which the lossmodulus of the material doubled). Although the time required printingthe 72-layered honeycomb was approximately only 35 minutes, withoutusing the mixing nozzle the extra time necessary for materialpreparation would have exceeded 10 minutes, potentially jeopardizing theprint. Hence use of the IDAM overcame this time constraint and couldhave facilitated 3D printing over far longer periods or in continuousoperation if necessary. Furthermore, the mixing chamber reduced theamount of wasted material, by requiring only the volume of materialnecessary for the structure to be mixed, and thereby leaving theunprinted resin and curing agent separate and available for futureprinting.

The above experimental results are based on the following methods:

Fluid Preparation

The water:glycerol [20:80 wt %] mixture was prepared from deionizedwater and glycerol (Macron). The aqueous polymer lubricant (Klein Tools)was obtained commercially, and the pluronic aqueous solution wasprepared by adding 30 wt % pluronic F-127 (Sigma Aldrich) to deionizedwater and dissolved at 4° C. for 48 hours before use. A red moleculartracer dye (IFWB-C7, Risk Reactor) was added to 40 mL batches of eachfluid at approximately 1 μL/gram, corresponding to 0.025 wt % dye. Tomeasure the mixing of non-Brownian particles 6-μm tracer particles(Fluoro-Max Thermo Scientific) at 0.04 wt % were added topolydimethylsiloxane (SE 1700, Dow Corning).

To demonstrate 3D printing with variable color, a stream of clear andpigmented (1 wt % red silicone pigment, SmoothOn) 10:1 resin:curingagent SE 1700 were mixed. The resin of the two-part epoxy used to printhoneycomb structures was composed of 87 wt % EPON 828 (Momentive), 9 wt% TS-720 fumed silica (Cabot), 4 wt % blue epoxy pigment (System 3). Thecuring agent was composed of 90 wt % Epikure 3234 (Momentive) 10 wt %TS-720 fumed silica (Cabot).

Fluid Rheology

The viscosity of each test fluid was measured with a stress-controlledrotational rheometer (AR2000ex, TA Instruments). At shear rates above{dot over (γ)}≳1 s⁻¹, material was ejected from the gap due to edgefracture preventing reliable measurements at higher shear rates.Alternatively, a custom capillary rheometer was used to measure theviscosity at shear rates 1≲{dot over (γ)}≲1000 s⁻¹. This systemconsisted of a syringe pump (PHD Ultra, Harvard Apparatus), 1.0 mL glassLuer lock syringe (Hamilton Gastight), a diaphragm pressure transducer(PX44E0-1KGI, Omega Engineering) and disposable Luer lock needle tips(Norsdon EFD). The pressure drop across the capillary tips was measuredover a range of flow rates. The Bagely correction and theWeissenberg-Rabinowitsch correction were applied to determine theresultant flow curves shown in FIG. 10.

FIG. 10 illustrates rheological flow curves of the three inkformulations used in calibration tests in this work. Data taken with therotational rheometer (filled symbols) and the capillary rheometer(hollow symbols) are shown. The black solid lines are the respectivefits of the Herschel-Bulkley model given by the fitting parameterslisted in Table 1.

Measurement of Diffusion Coefficients:

The molecular diffusion coefficient of the IFWB-C7 dye (rhodamine-WT,absorption/emission: 550/588 nm, Risk Reactor) was measured in theaqueous solutions using a custom Y-type rectilinear capillary channelwith inner dimensions h×w=900×900 μm (Vitrocom). The channel wassubmerged in immersion oil (n=1.48, Type FF, Cargille) to minimizerefraction, illuminated with a mercury lamp (local emission peak at 546nm) and visualized through a TRITC filter cube (peak transmittance580-630 nm) using a QColor 5 camera (Olympus) and a 10× objective on aninverted epifluorescence microscope (Olympus IX71). Calibrationmeasurements were taken to relate the intensity of the emitted light tothe dye concentration and at each pixel to account for spatialvariations in the illumination intensity. During each measurement, astream of dyed fluid and a second stream of undyed fluid were pumped atequal flow rates into the channel. Once a sharp interface between thetwo streams had stabilized at the channel midplane, the pumping wasstopped and the subsequent evolution of the concentration profile acrossthe width of the channel was recorded at 1 cm downstream from theY-junction.

The evolution equation for the concentration C(x,t) across the channelis

$\frac{\partial C}{\partial t} = {{??}\frac{\partial^{2}C}{\partial x^{2}}}$where x is the spatial coordinate, t is time and

is the molecular diffusion coefficient. The initial condition for theexperiments in the capillary channel is C(x,0)=C₀H(x), where C₀ is theinitial concentration in the first stream and H(x) is the Heavisidefunction. There are no flux boundary conditions at both walls, ∂C/∂x=0at x=±w/2. The concentration profile is given by

$\begin{matrix}{\frac{C\left( {x,t} \right)}{C_{0}} = {\frac{1}{2}\left\{ {1 + {4{\sum\limits_{n\;{odd}}^{\infty}{\frac{1}{n\;\pi}{\sin\left( {n\;\pi\frac{x}{w}} \right)}{\exp\left( {\left( {n\;\pi} \right)^{2}\frac{{??}\; t}{w^{2}}} \right)}}}}} \right\}}} & (15)\end{matrix}$The value of D was determined from the average of multiple fits of Eq.(15) to the measured concentration profiles at multiple positions alongthe channel width (x=±⅓, ¼, ⅕x/w). An example concentration profile isshown in FIG. 11.

FIG. 11 shows measurements of the diffusion coefficient of the IFWB-C7dye (rhodamine-WT, Risk Reactor) at 23° C. FIG. 11A is a top view of thecapillary with the injected dyed and undyed streams. FIG. 11B is aspatiotemporal plot of experimentally measured dye concentration [g/L]in water (viscosity μ=0.001 Pa·s). FIG. 11C shows evolution of theconcentration at x=−180 μm (top solid curve) and x=180 μm (bottom solidcurve). The white-dot curves are the fit of C(x,t) from Eq. (15) withx=±180 μm, w=900 μm, C₀=0.13 g/L and

=500 μm²/s. The Stokes-Einstein equation was used to estimate themolecular diameter of the tracer dye d_(p)=k_(B)T/3πμ

=0.87 nm.

For this study, a particle was considered Brownian if the ratio ofthermal stresses acting on a particle to viscous stresses in theNewtonian fluids or the yield stress of the viscoelastic ink(Λ₁≡k_(B)Td/μUd_(p) ³, and Λ₂≡k_(B)T/d_(p) ³τ_(y), respectively) farexceeded unity, where k_(B) is the Boltzman constant, T is the absolutetemperature, μ is the fluid viscosity, d_(p) is the particle diameter,and τ_(y) is the yield stress. Measurements of the diffusion coeeficient

of the dye used in this study (FIG. 11) indicated that its moleculardiameter was approximately d_(p)=0.87 nm. For T=295 K, μ=1.2 Pa·s(glycerol), U˜1 m/s (maximum print speed), and τ_(y)=500 Pa (pluronic),the ratios Λ₁˜0(10³) and Λ₂˜0(10⁴), which confirmed the dominance ofthermal forces on the dye molecules. Conversely, for the d_(p)=6 μmfluorescent particles, Λ₂˜0(10⁸) <<1 and hence the particles werenon-Brownian.

Nozzle Manufacture

Passive mixing chambers were machined from two poly (methylmethacrylate) (PMMA) polymer blocks using a CNC-mill (8540, SherlineProducts Inc.). The grooves were milled with a 200-μm end mill(Ultra-Tool International), while all larger features were milled with a3-mm end mill. Luer lock connectors were added to each block. A 480-μmthick plastic (PETG) shim stock (Artus Corp.) was machined and used as aspacer between the two PMMA blocks, which were bolted together to ensurea tight seal. An optical image of one of the passive mixing chambersused in this study is shown in FIG. 9 along with expanded views of thewalls of the passive mixing chamber. For both designs, the channeldimensions were l=15 mm and d=500 μm. In the grooved wall mixingchamber, the spacing between 120 μm wide grooves positioned 45° relativeto the primary direction of flow was λ=200 μm. The net volume of themixing chamber was 3.6 μL, and thus the mixing chamber could be purged(to change extrudate composition) in approximately 15 mm of printedmaterial.

The active mixing chamber was fabricated by attaching two 1.54-mmdiameter (gauge 14, Nordsen EFD) needle tips into a threaded plasticmale Luer lock connector. The tips were then glued in place to preventleakage. The connector was attached to a PMMA block that was mounted tothe nozzle superstructure. The impeller was made from a 0.109-inchdiameter reamer (Alvord-Polk Tools) that was ground down to fit withinthe plastic tip of the nozzle. Notches were added to one of theimpellers to enhance mixing. A stepper motor drove the impeller shaft,which was sealed using an O-ring. A second active mixing chamber usingmetal Luer lock components (FIG. 12A is a picture of the superstructureused to hold the nozzle during printing, and FIG. 12B is a magnifiedimage of the metal nozzle used for printing the viscous two-part epoxy.)was fabricated to tolerate the higher pressures necessary for thetwo-part epoxy. The overall dimensions of this mixing nozzle were l=30mm and d=4 mm, and the impeller diameter was δ=2.7 mm. The volume of theactive mixing chamber was approximately 150 μL. Hence for a nozzle withtip diameter a=500 μm, at least 760 mm of printed material are requiredto purge the mixing chamber.

Flow Visualization, Imaging and Mixing Quantification:

In order to image the concentration distribution of the fluorescenttracer dye in the nozzle cross-section, the test fluids were extrudedonto a transparent petri dish under which a uEye camera (ImagingDevelopment Systems) was positioned and recording. Flow rates were inthe range 0.006≤Q≤20 mL/min. The rotational speeds of the impeller werein the range Ω=0, 0.01≤Ω≤30 rad/s (Ω=0, 0.095≤Ω≤286 rpm). The imageswere subsequently analyzed in Matlab to determine the uniformity of theconcentration profile. The mean I_(mean) and standard deviation I_(std)of the color saturation level (passive mixing chamber) or the intensityof the red channel (active mixing chamber) in the image was calculatedto determine the coefficient of variation v_(v)≡I_(std)/I_(mean), andthereby the uniformity of mixing.

The distributions of non-Brownian fluorescent particles in the printedSE 1700 filaments were measured with a 10× objective on an invertedepifluorescence microscope (Olympus IX71) using a QColor 5 camera(Olympus). A Matlab script written by the authors was used to determinethe Shannon entropy index of the particles s_(i)=Σ_(j=1) ^(k)P(x_(j)) lnP(x_(j)) where P(x_(j)) is the probability of finding a particle in thej^(th)-bin for the probability density function with k bins. Each bincorresponded to 20-μm sections of the printed filament. Referring to Eq.(14) the measured entropy of the printed filament is s_(f). The entropyof a hypothetically perfectly mixed filament is s_(m), for whichparticles are uniformly distributed, hence P(x_(j))=k⁻¹. The entropy ofa completely unmixed filament is s_(u), for which particles areuniformly present in only half the filament width, so P(x_(j))=0 forj≤½k and P(x_(j))=2k⁻¹ for j>½k.

Printing Control

For all tests and prints the nozzle was fixed in the lab frame and heldby a superstructure. Movement of the substrate was controlled by ahigh-precision XYZ air bearing gantry (Aerotech, Inc.). The inks werecontained in 3, 5 or 10 mL plastic syringes (Becton Dickinson) anddriven by two opposed syringe pumps (PHD Ultra, Harvard Apparatus) thatwere controlled directly by the NView HMI software (Aerotech, Inc.).

Accordingly, the present disclosure provides 3D printers withmicrofluidic active mixing nozzles for three-dimensional printing ofviscoelastic inks. The disclosures also provide methods of operating the3D printers. The disclosure provides tested simple scaling relationshipsgoverning the performance of an active mixing system utilizing arotational impeller. The present disclosure provides an improvedtechnology to control the mixing intensity independently from the flowrate.

While exemplary embodiments of the present disclosure relate to 3Dprinters with microfluidic active mixing nozzles for three-dimensionalprinting of viscoelastic inks, the devices and methods may also beapplied to other applications. For example, in addition to a 3D printer,the devices and methods may also be applied to other equipment thatmixes two or more fluids, such as cements in the construction industryor ice creams, coffee, or liquid chocolate in the food industry. Thepresent disclosure intends to cover the broadest scope of systems andmethods for mixing multiple fluids together.

Further, in the present disclosure, subject matter described therein iswith reference to the accompanying drawings, which form a part hereof,and which show, by way of illustration, specific exemplary embodiments.Subject matter may, however, be embodied in a variety of different formsand, therefore, covered or claimed subject matter is intended to beconstrued as not being limited to any exemplary embodiments set forthherein; exemplary embodiments are provided merely to be illustrative.Likewise, a reasonably broad scope for claimed or covered subject matteris intended. Among other things, for example, subject matter may beembodied as methods, devices, components, or systems. The above detaileddescription is, therefore, not intended to be limiting on the scope ofwhat is claimed.

Throughout the specification and claims, terms may have nuanced meaningssuggested or implied in context beyond an explicitly stated meaning.Likewise, the phrase “in one embodiment” as used herein does notnecessarily refer to the same embodiment and the phrase “in anotherembodiment” as used herein does not necessarily refer to a differentembodiment. It is intended, for example, that claimed subject matterincludes combinations of exemplary embodiments in whole or in part.

In general, terminology may be understood at least in part from usage incontext. For example, terms, such as “and”, “or”, or “and/or,” as usedherein may include a variety of meanings that may depend at least inpart upon the context in which such terms are used. Typically, “or” ifused to associate a list, such as A, B or C, is intended to mean A, B,and C, here used in the inclusive sense, as well as A, B or C, here usedin the exclusive sense. In addition, the term “one or more” as usedherein, depending at least in part upon context, may be used to describeany feature, structure, or characteristic in a singular sense or may beused to describe combinations of features, structures or characteristicsin a plural sense. Similarly, terms, such as “a,” “an,” or “the,” again,may be understood to convey a singular usage or to convey a pluralusage, depending at least in part upon context. In addition, the term“based on” may be understood as not necessarily intended to convey anexclusive set of factors and may, instead, allow for existence ofadditional factors not necessarily expressly described, again, dependingat least in part on context.

Thus, exemplary embodiments illustrated in the figures serve only asexamples to illustrate several ways of implementation of the presentdisclosure. They should not be construed as to limit the spirit andscope of the exemplary embodiments of the present disclosure. It shouldbe noted that those skilled in the art may still make variousmodifications or variations without departing from the spirit and scopeof the exemplary embodiments. Such modifications and variations shallfall within the protection scope of the exemplary embodiments, asdefined in attached claims.

The invention claimed is:
 1. A device for three-dimensional inkdeposition from an impeller-driven active mixing microfluidic printingnozzle, the device comprising: a microfluidic printing nozzlecomprising: a mixing chamber; and an impeller rotatably disposed in themixing chamber to mix a plurality of fluids to form a mixed ink; anelectronic controller in electrical communication with the printingnozzle, the controller configured to: receive a material propertyassociated with each of the plurality of fluids; receive a structureproperty of the printing nozzle; receive a predetermined volumetric flowrate Q of the plurality of fluids in the mixing chamber; determine athreshold rotating speed Ω of the impeller based on the materialproperty of the plurality of fluids, the structure property of theprinting nozzle, and the predetermined volumetric flow rate Q; introducethe plurality of fluids into the mixing chamber at the predeterminedvolumetric flow rate; and rotate the impeller with a rotating speedhigher than the threshold rotating speed Ω to mix the plurality offluids, thereby forming the mixed ink.
 2. The device of claim 1, whereinthe material property comprises a diffusion transport rate

of the plurality of fluids and a degree of completeness of mixture ε ofthe plurality of fluids, and the structure property of the nozzlecomprises a length l of the mixing chamber, a diameter d of the mixingchamber, and a diameter δ of the impeller.
 3. The device of claim 2,wherein, when an inner surface of the mixing chamber and an outersurface of the impeller are configured to enable laminar flow of theplurality of fluids, the threshold rotating speed of the impeller takesa form of:${\Omega = {\frac{Q}{\;{{ld}^{2}\alpha}}\sqrt{\frac{{c\;}_{1}ɛ\; Q}{\;{l\;\alpha\;{??}}}}}},$wherein $\alpha = \left( {1 - \frac{\delta^{2}}{d^{2}}} \right)$  and c₁is a constant value.
 4. The device of claim 2, wherein, when an innersurface of the mixing chamber and an outer surface of the impeller areconfigured to enable chaotic flow of the plurality of fluids, thethreshold rotating speed of the impeller takes a form of:${\Omega = {\frac{Q}{\alpha\;{ld}^{2}}\log_{4}\frac{c_{2}ɛ\; Q}{\alpha\; l\;{??}}}},$wherein $\alpha = \left( {1 - \frac{\delta^{2}}{d^{2}}} \right)$  and c₂is a constant value.
 5. The device of claim 2, wherein, when at leastone of the plurality of fluids includes non-Brownian particles, thematerial property associated with the at least one plurality of fluidsfurther comprises particle size d_(p) of the non-Brownian particles, andthe threshold rotating speed of the impeller takes a form of:${\Omega = {\frac{c_{3}ɛ\; Q}{\alpha\; l\; d^{2}}\ln\frac{d}{d_{p}}}},$wherein $\alpha = \left( {1 - \frac{\delta^{2}}{d^{2}}} \right)$  and c₃is a constant value.
 6. The device of claim 1, wherein the controller isfurther configured to: introduce the plurality of fluids via a pluralityof fluids inlets in communication with the mixing chamber; and rotatethe impeller by an electric motor operationally coupled to the impellerand electrically controlled by the controller; extrude a filament ofmixed ink over a substrate; and move at least one of the nozzle and thesubstrate in a predetermined way to form a predesigned 3D structureusing the mixed ink.
 7. The device of claim 6, wherein the 3D structurecomprise a soft robot.
 8. The device of claim 1, wherein the mixed inkcomprises an elastomeric ink.
 9. A method for three-dimensional inkdeposition from an impeller-driven active mixing microfluidic printingnozzle, the method comprising: providing a microfluidic printing nozzlecomprising: a mixing chamber; and an impeller rotatably disposed in themixing chamber to mix a plurality of fluids to form a mixed ink;receiving by a controller in electrical communication with the printingnozzle: a material property associated with each of the plurality offluids; a structure property of the printing nozzle; a predeterminedvolumetric flow rate Q of the plurality of fluids in the mixing chamber;determining a threshold rotating speed Ω of the impeller based on thematerial property of the plurality of fluids, the structure property ofthe printing nozzle, and the predetermined volumetric flow rate Q;introducing the plurality of fluids into the mixing chamber at thepredetermined volumetric flow rate; and rotating, under control of thecontroller, the impeller with a rotating speed higher than the thresholdrotating speed 106 to mix the plurality of fluids, thereby forming themixed ink.
 10. The method of claim 9, wherein the material propertycomprises a diffusion transport rate

of the plurality of fluids and a degree of completeness of mixture ε ofthe plurality of fluids, and the structure property of the nozzlecomprises a length l of the mixing chamber, a diameter d of the mixingchamber, and a diameter δ of the impeller.
 11. The method of claim 10,wherein, wherein, when an inner surface of the mixing chamber and anouter surface of the impeller are configured to enable laminar flow ofthe plurality of fluids, the threshold rotating speed of the impellertakes a form of:${\Omega = {\frac{\; Q}{l\; d^{2}\alpha}\sqrt{\frac{c_{1}ɛ\; Q}{l\;\alpha\;{??}}}}},$wherein $\alpha = \left( {1 - \frac{\delta^{2}}{d^{2}}} \right)$  and c₁is a constant value.
 12. The method of claim 10, wherein, when an innersurface of the mixing chamber and an outer surface of the impeller areconfigured to enable chaotic flow of the plurality of fluids, thethreshold rotating speed of the impeller takes a form of:${\Omega = {\frac{Q}{\alpha\;{ld}^{2}}\log_{4}\frac{c_{2}ɛ\; Q}{\alpha\; l\;{??}}}},$wherein $\alpha = \left( {1 - \frac{\delta^{2}}{d^{2}}} \right)$  and c₂is a constant value.
 13. The method of claim 10, wherein, when at leastone of the plurality of fluids includes non-Brownian particles, thematerial property associated with the at least one plurality of fluidsfurther comprises particle size d_(p) of the non-Brownian particles, andthe threshold rotating speed of the impeller takes a form of:${\Omega = {\frac{c_{3}ɛ\; Q}{\alpha\; l\; d^{2}}\ln\frac{d}{d_{p}}}},$wherein $\alpha = \left( {1 - \frac{\delta^{2}}{d^{2}}} \right)$  and c₃is a constant value.
 14. The method of claim 10, further comprising:introducing the plurality of fluids via a plurality of fluid inlets incommunication with the mixing chamber; rotating the impeller by anelectric motor operationally coupled to the impeller and electricallycontrolled by the controller; extruding a filament of mixed ink over asubstrate; and moving at least one of the nozzle and the substrate in apredetermined way to form a predesigned 3D structure using the mixedink.
 15. The method of claim 14, wherein the 3D structure comprise asoft robot.
 16. The method of claim 9, wherein the mixed ink comprisesan elastomeric ink.
 17. A device for three-dimensional ink depositionfrom an impeller-driven active mixing microfluidic printing nozzle, thedevice comprising: a microfluidic printing nozzle comprising: a mixingchamber; and an impeller rotatably disposed in the mixing chamber to mixa plurality of fluids to form a mixed ink; an electronic controller inelectrical communication with the printing nozzle, the controllerconfigured to: receive a material property associated with the pluralityof fluids; receive a structure property of the printing nozzle; receivea predetermined rotating speed Ω of the impeller; determine a thresholdvolumetric flow rate Q of the plurality of fluids in the mixing chamberbased on the material property of the plurality of fluids, the structureproperty of the printing nozzle, and the predetermined rotating speed ofthe impeller; introduce the plurality of fluids into the mixing chamberat volumetric flow rate lower than the threshold volumetric flow rate Q;and rotate the impeller at the predetermined rotating speed Ω to mix theplurality of fluids thereby forming the mixed ink.
 18. The device ofclaim 17, wherein the material property comprises a diffusion transportrate

of the plurality of fluids and a degree of completeness of mixture ε ofthe plurality of fluids, and the structure property of the nozzlecomprises a length l of the mixing chamber, a diameter d of the mixingchamber, and a diameter δ of the impeller.
 19. The device of claim 17,wherein, when an inner surface of the mixing chamber and an outersurface of the impeller are configured to enable laminar flow of theplurality of fluids, the threshold volumetric flow rate of the pluralityof fluids takes a form of:${Q = {\alpha\;{{ld} \cdot \sqrt[3]{\frac{d\;{??}\;\Omega^{2}}{c_{1}ɛ}}}}},$wherein $\alpha = \left( {1 - \frac{\delta^{2}}{d^{2}}} \right)$  and c₁is a constant value.
 20. The device of claim 18, wherein, when an innersurface of the mixing chamber and an outer surface of the impeller areconfigured to enable chaotic flow to the plurality of fluids, thethreshold volumetric flow rate of the plurality of fluids takes a formof:${{Q\;\log_{4}\frac{c_{2}ɛ\; Q}{\alpha\; l\;{??}}} = {\alpha\;{ld}^{2}\Omega}},$wherein $\alpha = \left( {1 - \frac{\delta^{2}}{d^{2}}} \right)$  and c₂is a constant value.